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pAn update of the most accessible introductory number theory text available, bFundamental Number Theory with Applications, Second Editionb presents a mathematically rigorous yet easy-to-follow treatment of the fundamentals and applications of the subject. The substantial amount of reorganizing makes this edition clearer and more elementary in its coverage.ppbNew to the Second Editionb pp- Removal of all advanced material to be even more accessible in scope pp- New fundamental material, including partition theory, generating functions, and combinatorial number theory pp- Expanded coverage of random number generation, Diophantine analysis, and additive number theory pp- More applications to cryptography, primality testing, and factoring pp- An appendix on the recently discovered unconditional deterministic polynomial-time algorithm for primality testing ppTaking a truly elementary approach to number theory, this text supplies the essential material for a first course on the subject. Plac

Fundamental Number Theory with Applications | Mollin Richard A. | Paperback | Twarda

emAn Introduction to the Theory of Numbersem by G. H. Hardy and E. M. Wright is found on the reading list of virtually all elementary number theory courses and is widely regarded as the primary and classic text in elementary number theory. Developed under the guidance of D. R. Heath-Brown, this Sixth Edition of emAn Introduction to the Theory of Numbersem has been extensively revised and updated to guide today's students through the key milestones and developments in number theory. pUpdates include a chapter by J. H. Silverman on one of the most important developments in number theory -- modular elliptic curves and their role in the proof of Fermat's Last Theorem -- a foreword by A. Wiles, and comprehensively updated end-of-chapter notes detailing the key developments in number theory. Suggestions for further reading are also included for the more avid reader. pThe text retains the style and clarity of previous editions making it highly suitable for undergraduates in mathematics from t

An Introduction to the Theory of Numbers | Hardy G. H. | Twarda | Twarda

pRight triangles are at the heart of this textbook's vibrant new approach to elementary number theory. Inspired by the familiar Pythagorean theorem, the author invites the reader to ask natural arithmetic questions about right triangles, then proceeds to develop the theory needed to respond. Throughout, students are encouraged to engage with the material by posing questions, working through exercises, using technology, and learning about the broader context in which ideas developed.p Progressing from the fundamentals of number theory through to Gauss sums and quadratic reciprocity, the first part of this text presents an innovative first course in elementary number theory. The advanced topics that follow, such as counting lattice points and the four squares theorem, offer a variety of options for extension, or a higher-level course the breadth and modularity of the later material is ideal for creating a senior capstone course. Numerous exercises are included throughout, many of which a

A Pythagorean Introduction to Number Theory | Takloo | Bighash Ramin | Twarda

Ideal for a first course in number theory, this lively, engaging text requires only a familiarity with elementary algebra and the properties of real numbers. Author Underwood Dudley, who has written a series of popular mathematics books, maintains that the best way to learn mathematics is by solving problems. In keeping with this philosophy, the text includes nearly 1,000 exercises and problems--some computational and some classical, many original, and some with complete solutions. brThe opening chapters offer sound explanations of the basics of elementary number theory and develop the fundamental properties of integers and congruences. Subsequent chapters present proofs of Fermat's and Wilson's theorems, introduce number theoretic functions, and explore the quadratic reciprocity theorem. Three independent sections follow, with examinations of the representation of numbers, diophantine equations, and primes. The text concludes with 260 additional problems, three helpful appendixes, and

Elementary Number Theory | Dudley Underwood | Paperback | Twarda

This textbook presents an elementary introduction to number theory and its different aspects approximation of real numbers, irrationality and transcendence problems, continued fractions, diophantine equations, quadratic forms, arithmetical functions and algebraic number theory.These topics are covered in 12 chapters and more than 200 solved exercises.Clear, concise, and self-contained, this textbook may be used by undergraduate and graduate students, as well as highschool mathematics teachers. More generally, it will be suitable for all those who are interested in number theory, this fascinating branch of mathematics.

Number Theory | Duverney Daniel | Twarda

Natural numbers are the oldest human invention. This book describes their nature, laws, history and current status. It has seven chapters. The first five chapters contain not only the basics of elementary number theory for the convenience of teaching and continuity of reading, but also many latest research results. The first time in history, the traditional name of the Chinese Remainder Theorem is replaced with the Qin Jiushao Theorem in the book to give him a full credit for his establishment of this famous theorem in number theory. Chapter 6 is about the fascinating congruence modulo an integer power, and Chapter 7 introduces a new problem extracted by the author from the classical problems of number theory, which is out of the combination of additive number theory and multiplicative number theory.One feature of the book is the supplementary material after each section, there by broadening the reader's knowledge and imagination. These contents either discuss the rudiments of some asp

A Modern Introduction to Classical Number Theory | Cai Tianxin | Twarda | Twarda

Algebraic coding theory is a new and rapidly developing subject, popular for its many practical applications and for its fascinatingly rich mathematical structure. This book provides an elementary yet rigorous introduction to the theory of error-correcting codes. Based on courses given by the author over several years to advanced undergraduates and first-year graduated students, this guide includes a large number of exercises, all with solutions, making the book highly suitable for individual study.

A First Course in Coding Theory | Hill Raymond | Twarda

pstrongemElementary Number Theoryemstrong, Gove Effinger, Gary L. MullenppThis text is intended to be used as an undergraduate introduction to the theory of numbers. The authors have been immersed in this area of mathematics for many years and hope that this text will inspire students and instructors to study, understand, and come to love this truly beautiful subject.ppEach chapter, after an introduction, develops a new topic clearly broken out in sections which include theoretical material together with numerous examples, each worked out in considerable detail. At the end of each chapter, after a summary of the topic, there are a number of solved problems, also worked out in detail, followed by a set of supplementary problems. These latter problems give students a chance to test their own understanding of the material solutions to some but not all of them complete the chapter.ppThe first eight chapters discuss some standard material in elementary number theory. The remaining chapters 

Elementary Number Theory | Effinger Gove | Paperback | Twarda

This widely used textbook of modern formal logic now offers a number of new features. Incorporating updated notations, selective answers to exercises, expanded treatment of natural deduction, and new discussions of predicate- functor logic and the affinities between higher set theory and the elementary logic of terms, Quine's new edition will serve admirably both for classroom and for independent use.

Methods of Logic | Quine Willard Van Orman | Twarda

Algebra is primarily concerned with the study of mathematical symbols as well as the rules that operate such symbols. It is applied in most of the sub-domains within mathematics. Algebra makes use of letters to denote numerical values. Some of the major branches of algebra are elementary algebra and abstract algebra. Elementary algebra focuses on the study of variables and polynomials. Abstract algebra studies the abstraction such as groups, rings and fields as well as elementary equation solving. It is applied in the study of various fields such as algebraic topology and algebraic number theory. This book is compiled in such a manner, that it will provide in-depth knowledge about the theory and practice of algebra. Some of the diverse topics covered herein address the varied branches that fall under this category. Coherent flow of topics, student-friendly language and extensive use of examples make this book an invaluable source of knowledge.

Algebra | Houston Kevin | Twarda

pThis book offers an introduction to some combinatorial also, set-theoretical approaches and methods in geometry of the Euclidean space bRbimi. The topics discussed in the manuscript are due to the field of combinatorial and convex geometry. ppThe author's primary intention is to discuss those themes of Euclidean geometry which might be of interest to a sufficiently wide audience of potential readers. Accordingly, the material is explained in a simple and elementary form completely accessible to the college and university students. At the same time, the author reveals profound interactions between various facts and statements from different areas of mathematics the theory of convex sets, finite and infinite combinatorics, graph theory, measure theory, classical number theory, etc. ppAll chapters and also the five Appendixes end with a number of exercises. These provide the reader with some additional information about topics considered in the main text of this book. Naturally, the exer

Introduction to Combinatorial Methods in Geometry | Kharazishvili Alexander | Twarda | Twarda

pThis textbook provides an introduction to the mathematics on which modern cryptology is based. It covers not only public key cryptography, the glamorous component of modern cryptology, but also pays considerable attention to secret key cryptography, its workhorse in practice.p pModern cryptology has been described as the science of the integrity of information, covering all aspects like confidentiality, authenticity and non-repudiation and also including the protocols required for achieving these aims. In both theory and practice it requires notions and constructions from three major disciplines computer science, electronic engineering and mathematics. Within mathematics, group theory, the theory of finite fields, and elementary number theory as well as some topics not normally covered in courses in algebra, such as the theory of Boolean functions and Shannon theory, are involved.p Although essentially self-contained, a degree of mathematical maturity on the part of the reader is assu

Algebra for Cryptologists | Meijer Alko R. | Paperback | Twarda

pOne of the most pressingbbproblems of mathematics over the last hundred years has been the question What is a number One of the most impressive answers has been the axiomatic development of set theory. The question raised is Exactly what assumptions, beyond those of elementary logic, are required as a basis for modern mathematics Answering this question by means of the Zermelo-Fraenkel system, Professor Suppes' coverage is the best treatment of axiomatic set theory for the mathematics student on the upper undergraduate or graduate level. brThe opening chapter covers the basic paradoxes and the history of set theory and provides a motivation for the study. The second and third chapters cover the basic definitions and axioms and the theory of relations and functions. Beginning with the fourth chapter, equipollence, finite sets and cardinal numbers are dealt with. Chapter five continues the development with finite ordinals and denumerable sets. Chapter six, on rational numbers and real n

Axiomatic Set Theory | Suppes Patrick | Paperback | Twarda

What makes people smarter than computers These volumes by a pioneering neurocomputing group suggest that the answer lies in the massively parallel architecture of the human mind. They describe a new theory of cognition called connectionism that is challenging the idea of symbolic computation that has traditionally been at the center of debate in theoretical discussions about the mind. pThe authors' theory assumes the mind is composed of a great number of elementary units connected in a neural network. Mental processes are interactions between these units which excite and inhibit each other in parallel rather than sequential operations. In this context, knowledge can no longer be thought of as stored in localized structures instead, it consists of the connections between pairs of units that are distributed throughout the network. ppVolume 1 lays the foundations of this exciting theory of parallel distributed processing, while Volume 2 applies it to a number of specific issues in cogniti

Parallel Distributed Processing, Volume 1 | Rumelhart David E. | Twarda

pbr iNilpotence and Periodicity in Stable Homotopy Theoryi describes some major advances made in algebraic topology in recent years, centering on the nilpotence and periodicity theorems, which were conjectured by the author in 1977 and proved by Devinatz, Hopkins, and Smith in 1985. During the last ten years a number of significant advances have been made in homotopy theory, and this book fills a real need for an up-to-date text on that topic.pbr pRavenel's first few chapters are written with a general mathematical audience in mind. They survey both the ideas that lead up to the theorems and their applications to homotopy theory. The book begins with some elementary concepts of homotopy theory that are needed to state the problem. This includes such notions as homotopy, homotopy equivalence, CW-complex, and suspension. Next the machinery of complex cobordism, Morava K-theory, and formal group laws in characteristic ipi are introduced. The latter portion of the book provides specialists

Nilpotence and Periodicity in Stable Homotopy Theory. | Ravenel Douglas C. | Twarda

Intended to serve as a one-semester introductory course in number theory, this second edition has been revised throughout. In particular, the field of cryptography is highlighted. At the heart of the book are the major number theoretic accomplishments of Euclid, Fermat, Gauss, Legendre, and Euler. In addition, a wealth of new exercises have been included to fully illustrate the properties of numbers and concepts developed in the text. The book will serve as a stimulating introduction for students new to number theory, regardless of their background. First Edition Hb 1999 0-521-58503-1 First Edition Pb 1999 0-521-58531-7

Elementary Number Theory in Nine Chapters | Tattersall James J. | Paperback | Twarda

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pHow can music withstand the death and destruction brought on by war Global conflicts of the 20th century fundamentally transformed not only national boundaries, power relations, and global economies, but also the arts and culture of every nation involved. An important, unacknowledged aspect of these conflicts is that they have unique musical soundtracks. iMusic in World War IIi explores how music and sound took on radically different dimensions in the United States and Europe before, during, and after World War II. Additionally, the collection examines the impact of radio and film as the disseminators of the war's musical soundtrack. Contributors contend that the European and American soundtrack of World War II was largely one of escapism rather than the lofty, solemn, heroic, and celebratory mode of war music in the past. Furthermore, they explore the variety of experiences of populations forced from their homes and interned in civilian and POW camps in Europe and the United States, 

Music in World War II | Potter Pamela M. | Twarda

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